24^2+12^2=c^2

Solution for 24^2+12^2=c^2 equation:

24^2+12^2=c^2

We move all terms to the left:

24^2+12^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+720=0

a = -1; b = 0; c = +720;
Δ = b2-4ac
Δ = 02-4·(-1)·720
Δ = 2880
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{5}}{2*-1}=\frac{0-24\sqrt{5}}{-2}
=-\frac{24\sqrt{5}}{-2}
=-\frac{12\sqrt{5}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{5}}{2*-1}=\frac{0+24\sqrt{5}}{-2}
=\frac{24\sqrt{5}}{-2}
=\frac{12\sqrt{5}}{-1}
$